Stirling numbers of the second kind and Bell numbers are intimately
linked through the roles they play in enumerating partitions of
n-sets. In a previous article we studied a generalization of the
Bell numbers that arose on analyzing partitions of a special multiset.
It is only natural, therefore, next to examine the corresponding
situation for Stirling numbers of the second kind. In this paper we
derive generating functions, formulae and interesting properties of
these numbers.